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Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…
In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…
We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an…
In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…
We describe an approach to understand the peculiar and counterintuitive generalization properties of deep neural networks. The approach involves going beyond worst-case theoretical capacity control frameworks that have been popular in…
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous…
Machine learning promises methods that generalize well from finite labeled data. However, the brittleness of existing neural net approaches is revealed by notable failures, such as the existence of adversarial examples that are…
This paper proposes Quantizable DNNs, a special type of DNNs that can flexibly quantize its bit-width (denoted as `bit modes' thereafter) during execution without further re-training. To simultaneously optimize for all bit modes, a…
We introduce the DNNLikelihood, a novel framework to easily encode, through Deep Neural Networks (DNN), the full experimental information contained in complicated likelihood functions (LFs). We show how to efficiently parametrise the LF,…
Neural networks (NNs) are known to exhibit simplicity bias where they tend to prefer learning 'simple' features over more 'complex' ones, even when the latter may be more informative. Simplicity bias can lead to the model making biased…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
Deep neural networks are typically represented by a much larger number of parameters than shallow models, making them prohibitive for small footprint devices. Recent research shows that there is considerable redundancy in the parameter…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…
Considering uncertainty estimation of modern neural networks (NNs) is one of the most important steps towards deploying machine learning systems to meaningful real-world applications such as in medicine, finance or autonomous systems. At…
This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…
We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated…
We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves performing randomized measurements on a quantum processor…